To solve for $x$ in this triangle, we need to use the interior angle sum property of a triangle, which states that the sum of the interior angles of a triangle is always $180^\circ$.

Given angles:

1. $(x - 10)^\circ$
2. $(2x + 5)^\circ$
3. $35^\circ$

According to the angle sum property: $(x - 10) + (2x + 5) + 35 = 180$

Let's simplify and solve this equation.

Step-by-Step Solution

1. Combine like terms: $x - 10 + 2x + 5 + 35 = 180$ $3x + 30 = 180$

2. Subtract $30$ from both sides: $3x = 150$

3. Divide both sides by $3$: $x = 50$

Answer:

The value of $x$ is $50$.

Would you like a more detailed explanation of each step, or do you have any further questions?

Here are five related questions for further practice:

1. What would the angles be in this triangle if $x = 50$?
2. How would the solution change if one of the given angles was different?
3. Can we use the exterior angle property to solve for $x$ here?
4. How does the interior angle sum property apply to polygons with more than three sides?
5. What if one angle was given as a function of $y$ instead of $x$; how would we solve it?

Tip: Always remember to double-check that your sum equals $180^\circ$ when working with triangles!